标题： 拓扑绝缘体的分类：I. 非相互作用谱隙化的一维系统 显示英文标题

标题： Topological Classification of Insulators: I. Non-interacting Spectrally-Gapped One-Dimensional Systems

摘要： 我们研究在无序的一维材料中非相互作用的电子，这些材料表现出谱隙，并且属于十种Altland-Zirnbauer对称性类中的每一种。 我们在哈密顿量的空间上定义了一个适当的拓扑结构，使得所谓的强拓扑不变量成为完整的不变量，从而得出Kitaev周期表中的一维列，但现在无需借助K理论即可推导出该结果。 因此，我们确认了关于有能隙的非相互作用一维系统拓扑相与相应阿贝尔群$\{0\},\mathbb{Z},2\mathbb{Z},\mathbb{Z}_2$之间一一对应关系的猜想。 我们开发的主要工具是局部酉变换和正交投影的等变同伦理论。 此外，我们将酉理论扩展到部分等距变换，从而为理解强无序、迁移率间隙材料提供了一种视角。 显示英文摘要

摘要： We study non-interacting electrons in disordered one-dimensional materials which exhibit a spectral gap, in each of the ten Altland-Zirnbauer symmetry classes. We define an appropriate topology on the space of Hamiltonians so that the so-called strong topological invariants become complete invariants yielding the one-dimensional column of the Kitaev periodic table, but now derived without recourse to K-theory. We thus confirm the conjecture regarding a one-to-one correspondence between topological phases of gapped non-interacting 1D systems and the respective Abelian groups $\{0\},\mathbb{Z},2\mathbb{Z},\mathbb{Z}_2$ in the spectral gap regime. The main tool we develop is an equivariant theory of homotopies of local unitaries and orthogonal projections. Moreover, we extend the unitary theory to partial isometries, thus providing a perspective towards the understanding of strongly-disordered, mobility-gapped materials.